0:02 okay so this is the last part of our
0:04 first section of the school year end of
0:06 section 4.1 and we're going to learn
0:08 about another type of sampling technique
0:13 in this section so the new type of
0:16 technique is called a cluster sample and
0:17 let me go ahead before you guys get like
0:19 lost and reading my definition and
0:20 everything and walk you through a little
0:23 hypothetical example let's say I had a
0:26 big apartment complex with a lot of
0:27 units in it so it's like a lot of
0:30 separate buildings going on so I've got
0:32 all these little buildings in my
0:36 apartment complex right here and I want
0:38 to know what residents think about
0:40 raising the rents a little bit to build
0:43 a new pool so I wanna build a super cool
0:45 swimming pool right here and everybody's
0:46 gonna love it it's gonna be grades but I
0:48 got a raise rent a little bit to be able
0:52 to buy the pool so um I could go and
0:53 talk to every single resident and if I
0:55 didn't own that many buildings that
0:57 probably honestly is the most favorite
0:58 thing to do but let's say it's just a
1:00 big complex and I don't have that kind
1:03 of time so I'm just gonna take a random
1:06 sample instead I could do an SRS just
1:08 number off every person who is paying
1:11 rent to me and then choose randomly that
1:12 way and that would be great
1:14 I could also do some sort of a
1:17 stratified sample a good variable to
1:21 stratify by might be income if I pick
1:22 somebody has a lot of income maybe
1:24 they're willing to have a pool put in
1:26 where if they're not making as much that
1:28 may not be something that's worth the
1:30 expense for them so if I somehow add
1:33 access to their income levels I could
1:35 stratify by that get people at the high
1:37 income group medium medium low whatever
1:40 and pick some from each group and that
1:43 would be fine on a lot of times
1:45 stratified samples though are more
1:48 difficult to execute
1:51 compared to other sampling techniques so
1:53 like let's say I did do that by income I
1:55 might have to go over to this apartment
1:57 talk to that floor right there then go
1:58 all the way over to here and then go to
2:00 there and go to there and get all these
2:02 different apartments the same thing
2:04 would actually also happen in SRS I'd be
2:06 like running all over my complex talking
2:08 to these different people so they
2:11 introduced another valid sampling
2:13 technique called a cluster sample
2:17 and what a cluster sample does is it
2:19 breaks population up populations of all
2:22 my apartments residents here it breaks
2:25 them up into groups that are called
2:27 clusters based on proximity or something
2:30 that's already pre established so for
2:32 example in my apartment complex each
2:35 building is a nice little cluster
2:37 already um there are already bunch of
2:38 people in here a bunch of people in here
2:40 a bunch of people in here and I can
2:43 treat these like my separate units in my
2:46 problem now cluster sampling says that
2:48 what you do is instead of numbering off
2:50 people you're not gonna number off every
2:52 single apartment in there you just do
2:53 the building itself that's building one
2:55 building to building three building four
2:59 etc and you randomly choose your numbers
3:01 so you're gonna choose I chose number
3:03 three number seven number eleven those
3:06 are my buildings so what I would do once
3:08 I get my numbers is I would go and I
3:11 would use everybody in that building for
3:14 my sample everybody in that building for
3:18 my sample in a stratified sample I take
3:20 a little bit out of each separate group
3:23 in a cluster sample the randomness
3:25 happens from picking the group's
3:28 themselves but once I have my groups I
3:32 use everybody inside of that group this
3:33 can be a good thing
3:35 cluster sampling is good in the sense
3:37 that it's easier people are already in
3:39 buildings if I own this giant complex I
3:40 don't have to run around everywhere I
3:42 just go to the buildings that I chose
3:45 and use those people it doesn't work out
3:47 very well though if the buildings are
3:50 different in some fashion so cluster
3:53 sampling kind of assumes that this
3:54 building is the same as this building is
3:56 the same as this building one building
3:59 is as good as any other basically and
4:01 weirder for this to work well your
4:03 clusters need to represent many
4:06 populations so in order for this to be
4:20 okay so
4:22 talk about some ways that my little
4:23 apartment the example wouldn't be so
4:26 great what if I had a bunch of fancier
4:28 apartments like luxury apartments in one
4:29 of the buildings like say building
4:31 number one was like really fancy
4:33 apartments and I chose that building for
4:36 my sample well if this building is
4:38 different than the other ones those
4:39 people will think differently and that's
4:41 not good I'm gonna get biased in my
4:43 results or possibly or certainly
4:45 increased variability between different
4:47 samples so if you have buildings that
4:50 are different it won't work out so great
4:52 every building is supposed to be about
4:55 the same if I would have thought that Oh
4:56 each building is different I could pick
4:59 some from each and do a stratified
5:02 samples so cluster sampling works if the
5:04 buildings are more or less similar to
5:06 one another why do we do it I've already
5:08 talked about this it's usually more
5:10 efficient and easier to execute compared
5:12 to a stratified sample it's easier to
5:14 walk into one building and talk to
5:15 everybody that it is to run around and
5:17 do a little bit of each keeping these
5:20 two techniques straight is gonna be
5:22 really important for you guys um so I
5:24 have a little thing that I use little
5:26 phrase I want you mister write down so
5:31 stratified versus cluster so a
5:35 stratified sample is going to be similar
5:48 with in and then difference between in
5:51 my example of that was my freshman my
5:55 sophomores my juniors my seniors with
5:58 you I don't know where are there s are
6:01 at senior each bubble as freshmen
6:03 probably feel about the same as
6:04 sophomores feel about the same juniors
6:06 feel about the same as each other
6:08 so all juniors think somewhat similarly
6:10 about the prom thing but juniors
6:13 compared to freshmen probably have
6:15 different opinions so the bubbles
6:17 themselves are very different but within
6:19 the bubble you're saying they're more or
6:22 less the same a cluster is going to be
6:24 the opposite of that's so clusters are
6:27 different within you're going to get
6:29 people from all walks of life
6:30 within so in the apartment building
6:31 you'll have some people with higher
6:33 income someone with lower presumably
6:39 but they're similar between both of
6:41 these are valid good sampling techniques
6:44 that are if used correctly can be better
6:47 than an SRS but um they take thoughts to
6:49 execute properly if you do a bad job
6:52 thinking through either these techniques
6:55 it's not gonna work out for you so I
6:56 have a big example to talk through the
6:58 different techniques here um and we're
7:00 looking at a library this library is
7:03 really big it has 20,000 books in it and
7:05 for some reason this library isn't
7:08 organized by section like by type of
7:10 book it's just a through Z so we got
7:12 like big ol shelves with the books
7:14 starting with authors a all the way
7:19 through Z first thing they ask us to do
7:21 is to just like describe in detail how
7:23 you would do an SRS and I have these
7:25 written out so I want to talk you
7:26 through this but you cannot ultimately
7:28 just write what I have right here you
7:30 can make a little paragraph like I did
7:33 or you can do like a list like that it's
7:35 up to you either way you can abbreviate
7:37 you can do whatever but there are
7:39 problems that ask you to talk in detail
7:41 about what you're going to do kids tend
7:43 to find these a little bit annoying
7:45 because you have to write a lot and then
7:48 you have to be fairly specific but in
7:50 general when they ask how to explain a
7:53 sample you need to make sure that you
7:56 are going to be super detailed so
7:57 explain how to select a simple random
8:03 sample detail is gonna be so key in this
8:05 class if there's one thing I write for
8:07 you want feedback again and again again
8:09 over the course of the year it's going
8:10 to be detail you need to make sure
8:12 you're being very specific and how you
8:14 use it is so talking through my library
8:17 I have 20,000 books the first thing I
8:19 should do is I should label each book
8:21 and give them a number so you can see
8:23 right here that I said assign each book
8:26 a unique number from 1 to 20 thousands
8:30 that word unique is key in this problem
8:32 it's kind of like a stupid thing but
8:34 like if I just say oh give everybody a
8:37 number from 1 to 20,000 what if they use
8:39 numbers repeatedly oh that's one that's
8:42 one that's one by adding in the word
8:44 unique you're making sure they're not
8:46 being like ridiculous and how they are
8:48 setting up their tables right here so
8:50 the first thing you do when you're asked
8:52 to write one of these problems is you
8:54 talk about labels you need to make sure
8:56 you specify they're unique
9:01 then you need to talk about how to get
9:07 your random numbers this is grand
9:09 numbers right there so I'm gonna use a
9:11 calculator I'm gonna use the command R
9:14 and n so 1 comma 20,000 s and I'm gonna
9:18 select 500 unique numbers again I use
9:20 the word unique it's a great word for
9:21 this because it means you don't repeat
9:23 things but even so you need to be very
9:25 explicit and I just go ahead and say
9:27 reject repeats or throw out repeated
9:30 numbers so you also need when you do one
9:31 of these problems to talk about what
9:35 happens to read beats and I don't want
9:37 to repeat a book when I'm making my
9:40 sample and finally you're gonna stop
9:41 talk about what you would actually do
9:44 your action I am going to look at the
9:47 number of pages in each book so writing
9:49 these out to be specific enough you have
9:51 to do these four things it's kind of a
9:53 lot and it's a little bit annoying to
9:55 write it out I sympathize with you there
9:56 I don't super love writing them in
9:59 detail but the AP test will do this to
10:00 make sure you truly understand what it
10:05 takes to collect rain all right so
10:08 second thing is a stratified sample in a
10:10 stratified sample in the same context
10:12 you would have to think about a variable
10:14 that measures from what makes a
10:17 difference in how long a book is and one
10:19 thing that they kind of fed you in the
10:20 problem there was they mentioned the
10:22 word genre and put that in your head it
10:25 seems plausible to me like think about
10:26 like a comic book or a magazine that
10:28 type of genre is gonna have a different
10:30 amount or even like a little young adult
10:33 fiction novel compared to a big history
10:35 textbook or a big encyclopedia or
10:37 something like that so the type of book
10:39 presumably makes a difference in how
10:43 many pages it has so what I could do
10:45 them instead of one big list I would
10:47 take all my history books number them
10:50 off to one to whatever all my fiction
10:53 books 1 2 whatever all my I don't know
10:55 whatever kind of books there are and I
10:58 would pick some randomly out of each
11:00 group now when you do astray
11:03 example you don't always have to do the
11:06 same allowance in each group let's say
11:07 when I'm doing this problem I have like
11:12 I know tons and tons of fiction books
11:16 but my little encyclopedia pile is
11:19 actually smaller you can pick them with
11:21 print look in proportion to the actual
11:24 population like let's say for example
11:26 50% of the books in this library are
11:29 fiction and only 10% are encyclopedias I
11:31 could make it so 10% of my sample is
11:34 encyclopedias and 50% is fiction
11:36 so you can pick with respect to the
11:38 population that's totally cool but in
11:40 this problem a good variable to stratify
11:43 by would probably be the genre other
11:45 things kids have thrown my way over the
11:47 years um where they are on the shelves
11:49 presumably you're not putting a giant
11:50 massive things like this way on the top
11:53 shelf it's somebody in the head so
11:54 somebody said couldn't you do like the
11:57 bottom shelf as one strata and the next
11:58 shelf in the next shelf that's a
12:01 possibility - there's a lot of things
12:03 you can do to stratify by genre was just
12:05 the first most obvious thing I can think
12:09 of so let's keep it going then and talk
12:11 about the same scenario with a cluster
12:14 sample the books are set up on shelves
12:17 of 50 and the way that I made my library
12:19 is maybe unrealistic because I said my
12:21 library is just straight-up alphabetical
12:23 not separated into genre like most
12:25 libraries are if it's straight up of
12:29 medical each shelf is probably one about
12:31 as good as the up that's not how most
12:32 libraries are like if I had all my
12:35 encyclopedias over here a cluster sample
12:37 would be a bad thing because this is not
12:40 the same as this but assuming that oh
12:42 yeah they are all about the same
12:44 if the shelves are similar than all I
12:46 would do is I would number off my
12:50 shelves 1 2 3 4 etc I would do a random
12:53 sample and pick my shelves and then once
12:54 I got my shelves I would talk to you
12:57 look at every book in that shelf so
12:58 that's how you could incorporate a
13:02 cluster sample so what is a drawback to
13:05 each method I'm talking specifically I
13:08 want to focus on the SRS is fine
13:10 SRS works well but the SRS and is
13:13 stratified in my library are making me wrong
13:13 wrong
13:15 the place to go find all those books
13:17 this cluster is going to be the easiest
13:21 of the three to execute because um I can
13:22 just go to one shelf and sit there and
13:25 like look at all of those books so the
13:27 cluster frequently going to be more
13:29 efficient still works well if the
13:32 clusters are legit but if the
13:33 bookshelves actually are different and
13:35 I'm making a bad assumption I can get
13:40 bad data that way so let's move on and
13:44 talk about this slide so this is a new
13:46 context right here now we're looking at
13:50 kids at a university and we want to know
13:54 what percent of students we're at class
13:55 every single day so what percent of
13:57 students didn't skip any of their
13:59 classes and the only difference between
14:02 these two pictures each dot is going to
14:04 be like a separate sample so it doesn't
14:05 say oh is it does it says I'm talking to
14:07 100 people that I'm talking to 400
14:10 people um so what this means because
14:13 this is honestly this simulation stuff
14:15 right here is one of the hardest parts
14:17 of all of ap stats we hit it again and
14:20 again and again in my first picture what
14:24 is going on is I have 500 dots in this
14:28 picture each of those dots is a separate
14:31 sample of 100 kids so I am going to
14:34 survey a hundred kids for my sample we
14:36 will get this dot right here at like
14:39 point 80 that will be a sample where I
14:42 took a hundred kids and 80 percent of
14:44 them went to class and then I would
14:46 throw those kids back in and pick
14:48 another sample of 100 kids and that time
14:52 oh gosh only 75% said yes and then the
14:54 next time I go over here I got 67% etc
14:58 etc etc each of those dots is a separate
15:02 group of a hundred kids and I do that
15:04 there are 500 dots in that picture
15:07 similarly in my second picture right
15:10 here still each of these dots is a
15:13 separate sample but they changed it so
15:16 now this is a sample of 400 kids so each
15:20 dot is a group of 400 kids instead of a
15:22 hundred kids like over here still 500
15:24 dots but it's a different shape to the
15:25 picture when you look at it it's
15:26 different spread anyway
15:29 so let's talk about what's going on here
15:32 when your sample size gets bigger the
15:34 whole thing this slide right here is
15:54 we've talked about the word variability
15:56 already um it's just talking about how
15:59 spread out things are the data tends to
16:01 be more consistent when your sample size
16:04 is bigger so let's say at the college
16:07 it's actually where 70% of kids went to
16:09 class every single day and it actually
16:11 says that the problem 70% of kids at
16:13 this school actually go to class without
16:15 skipping at every single day if I talk
16:17 to a hundred kids it could be where I
16:20 get a fluky sample where wow I got a lot
16:21 of really motivated kids here and I
16:23 happen to get like 83 of them who went
16:26 to school every single day it could also
16:28 be where I have a group of 100 and oh
16:31 less than usual I only got like 56% over
16:34 here so there's a lot more spread going
16:36 on in this picture than there is over
16:39 here if you get a sample of 400 you're
16:41 not gonna have as many of those fluky
16:43 things like if the answer is actually 70
16:47 getting an 85 isn't gonna happen if you
16:49 take a bigger sample because even if you
16:51 get like some kids that oh yeah I do go
16:54 to class you also get more that don't
16:57 and it kind of balances out so this note
16:59 right here is a really important one
17:02 when your sample is bigger your data
17:04 becomes more consistent if I take a
17:07 sample of 400 and you take a sample of
17:10 400 we're probably gonna get closer to
17:12 the same answer we will hit this again
17:14 and again and again as we go through
17:15 this class so no worries if that's
17:19 though a little shaky right now so let's
17:21 see what else we've got here remind
17:23 myself how much more I have all right
17:26 couple vocab words here inference is
17:29 basically all of second semester of ap
17:31 stats we're building up little pieces of
17:33 it now we really hit this hard second
17:35 semester when we talk about confidence
17:37 interval significance testing and so on
17:39 also inference means
17:43 he's using your sample to talk about the
17:45 whole population using results from a
17:47 little sample to apply to the whole
17:50 population that's what inference minutes
17:52 when you collect results you're not
17:55 always going to get the exact answer
17:56 that's called they did like you may be
17:59 off by a little bit just by chance when
18:01 I looked at my last slide right here um
18:04 the answer was 70% but I don't get
18:07 exactly 70 every time that we do it I
18:08 could be a little higher could be a
18:11 little lower the amount that I think I
18:13 could be off by the maximum amounts is
18:15 called the margin of error so if you
18:17 look at this problem it looks like most
18:19 of my data points are within five
18:22 percents of 70 whereas over here on the
18:24 second picture you can see it's a lot
18:27 more spread out it's more like 10% each
18:29 way or even a little higher than that so
18:31 the margin of error is lower on this
18:33 picture in all margin of error really
18:36 means is the maximum you think your
18:38 answer might be off line and when you
18:40 increase sample size it makes your
18:42 estimates more precise we've talked
18:44 about this already it decreases
18:49 variability between samples so let's go
18:51 ahead and talk about a few other things
18:53 with regards to simply that last part
18:56 rate with the pictures was a little bit
18:58 confusing this isn't so bad we want to
19:00 talk about a few other things that can
19:03 go wrong after you've selected or when
19:04 you've decided you're gonna select your
19:06 sample so okay I've convinced you that
19:08 your sample should be random
19:10 what happens now first one is called
19:15 under coverage and under coverage means
19:18 that some individuals were not actually
19:21 able to be chosen for your population
19:23 okay so some people were not able to be
19:27 chosen classic example there's a famous
19:29 newspaper picture that you might have
19:31 seen from like the 1940s
19:34 um it says Dewey defeats Truman it was
19:35 for the presidential race Dewey defeats
19:38 Truman Harry Truman is a presidents that
19:40 you guys have probably heard of I don't
19:41 even know doobies first name john maybe
19:45 um Thomas I'm not sure whoever he is
19:47 I've really thought he was gonna win it
19:48 was the night before the election and
19:50 the results weren't in yet but
19:52 newspapers back then had to print earlier
19:53 earlier
19:54 than they otherwise like before the
19:57 results were final but they felt so good
19:59 from their surveys that they actually
20:00 went ahead and said oh yeah doobies
20:02 totally gonna win and publish this
20:04 headline and it's picture of truman like
20:06 laughing looking at it after he actually
20:09 won the election what had happens there
20:11 were a couple of reasons but basically
20:13 one of them was they did a lot of their
20:16 surveying by phone so they called people
20:17 in this said hey who are you gonna vote
20:20 for well back in the 1940s having a
20:23 phone was that fancy thing so they ended
20:25 up talking to a lot more wealthy people
20:27 who were in favor of dewey and the
20:29 people who without phones who tended to
20:31 have less money voted for truman and
20:32 pushed him over the top and he ended up
20:35 winning that's under coverage because
20:37 some people people without phones
20:40 weren't able to be contacted that
20:41 happens all the time like if you do an
20:43 internet survey some people still don't
20:45 have access to the internet so you're
20:47 not gonna hear as much from people in
20:49 rural areas older people as a general
20:52 rule or people who can't afford to pay
20:54 for the regular internet access so
20:56 certain groups get left out if you're
20:58 not careful on where your data comes
21:00 from that's called under coverage the
21:03 next thing on here is called
21:07 non-response and non-respondents is when
21:10 you choose your sample random so you've
21:12 chosen your sample everything is cool
21:14 you contact people hey be in my sample
21:17 and they either say no or you can't get
21:20 in touch with them okay so this happens
21:22 a lot on we do a semester projects
21:24 related to sampling and people will like
21:26 email kids okay you've been chosen to be
21:29 in my survey and the kids like I don't
21:31 want to do that they ignore it that is
21:34 an issue because the kids who ignore
21:36 your survey may feel differently than
21:38 kids who respond so you still run the
21:42 issue of bias even though you did your
21:45 sample randomly this sounds a lot like
21:47 voluntary response which we talked about
21:50 earlier in this section the key
21:52 difference is that voluntary response
21:54 you just put out in general hey be and
21:56 my study if you want to you didn't do
21:59 anything random so voluntary response
22:01 there was no randomness you just let
22:03 people invite themselves non-response
22:06 occurs after you've selected your random
22:07 sample so you
22:09 the right thing and you randomly sampled
22:11 but then people didn't respond so what
22:13 would you do in that scenario in real
22:15 life if that happens well you try
22:17 contacting them again and try to get
22:19 them to follow up and be in the survey
22:21 and if they wouldn't you could randomly
22:23 pick somebody else but you can put like
22:24 a disclaimer that this many people
22:26 didn't respond because those people
22:28 could actually feel differently these
22:30 two things right here and many others
22:35 are examples of response bias response
22:38 bias is a general catch-all term for
22:41 things that might happen or that you
22:43 might do that might influence the
22:46 results or responses that you get so
22:52 response bias is as opposed to sampling
22:56 bias so your two main types of bias are
22:59 response bias and sampling bias actually
23:01 these two things right here I misspoke
23:02 and there you go those aren't really
23:04 response bias I'll give you some
23:07 examples of things that are so sampling
23:09 bias is bias and how you collected your
23:11 data in the first place response bias
23:15 can happen even if your results are your
23:17 results came from a random saying let me
23:19 give you a few quick examples the
23:20 wording on the question can lead people
23:23 to respond to a certain way so if I
23:25 think everybody at mrh to take four
23:27 years of math and set of three I can be
23:30 like hey given that colleges want to see
23:32 four years of math and math is an
23:34 essential tool for being great in life
23:36 and etcetera etc do you think we should
23:38 do four years of math instead of three
23:40 it doesn't matter if I was actually
23:43 random and who I talk to if you can tell
23:46 that I want it you may say yes just to
23:48 agree with me even if you don't actually
23:50 believe that yourselves so the way that
23:53 you were to question can matter we
23:55 actually do our first semester project
23:57 on response bias so this is something
23:58 you guys will get to practice on later
24:01 on in the semester one thing that kids
24:03 did that um a good project from a couple
24:05 of years ago they had a Google survey
24:07 about doesn't even really matter what it
24:09 was just a random survey and they had
24:12 the big textbox option and the little
24:14 text box option and they just wanted to
24:16 see if people would type more in the big
24:18 textbox and they actually did so
24:20 something as simple as the size of the
24:22 text box or the color that your question
24:25 is written or even the order of the
24:28 questions can influence responses I did
24:30 a little bit of that with you guys um in
24:32 the survey I gave you I played around
24:33 with the order of the questions and did
24:35 some things that counts his response
24:37 bias which we'll investigate later on
24:40 not in this video here um one more
24:42 really good example and then I'll move
24:45 on there was a survey where basically
24:48 people they asked people like how happy
24:50 are you with life overall that was like
24:51 one question they had you rate it so how
24:53 happy are you with life and then
24:55 followed it up with how many dates have
24:58 you been on in the past month and then
24:59 they reverse the order of the questions
25:01 and asked about the dates first and got
25:04 lower responses for the happiness with
25:06 life in general so something as simple
25:08 as like what ordered us things in can
25:12 make a difference in responses so let's
25:15 close this out by talking about these
25:17 couple of examples right here again
25:20 practicing vocabulary if you're not ever
25:22 sure on a vocab word don't say the word
25:24 and guess just describe it and that will
25:24 be fine
25:26 this is not so much of a buzz word class
25:28 where you have to know oh that's
25:30 voluntary response or non-response or
25:32 whatever but let's go through these if
25:34 you choose your sample out of a
25:36 telephone book that is going to be under
25:39 coverage there are people who do not
25:41 have a phone number in the book and you
25:43 won't be able to contact them as a
25:46 results so you finally get a hold of
25:48 your sample you choose your sample but
25:50 some people can't be don't return calls
25:52 that's non-response when they choose not
25:56 to be a part of your study right there
25:59 and then a few years just walking people
26:00 walking by on the sidewalk that is a
26:04 voluntary response so those are three
26:06 things that are all bad sampling
26:09 techniques alright this last question
26:11 and then we're done with this video here
26:12 I'm not gonna write this one but I'm
26:14 just going to talk through this they
26:17 wants to figure out they found that 84%
26:19 of people opposed banning disposable
26:25 diapers and then explain how the how
26:27 this like leads to bias anytime they
26:29 talk about bias you have to do those two
26:31 things what's the problem and what direct
26:32 direct
26:35 does this problem probably some things
26:37 so this person says is estimated diaper
26:41 disposable diapers are less than 2% less
26:44 than 2% of the trash and landfills in
26:49 contrast beverages are 21% of the trash
26:53 given that it's only 2% would it be fair
26:56 to ban disposable diapers so people are
26:58 gonna look at that like Oh 2% that's not
27:01 very much those drinks are way more so
27:03 no we shouldn't ban diapers that's ridiculous
27:03 ridiculous
27:06 this question right here is very much
27:08 pushing people towards the conclusion
27:12 that having a such a small percentage
27:14 banning it isn't going to make much of a
27:15 difference so the wording of this
27:17 question is very much pushing people to
27:20 say that no it's not that big of a deal
27:22 the wording suggests it's not a big deal
27:25 so people are gonna say oh don't ban
27:28 them and they're pushed in that
27:29 direction more than if they had asked
27:31 the question and just innocently and
27:34 neutrally so the actual percentage of
27:37 people who are in opposition this is
27:39 probably overestimating that it's
27:41 probably higher than the actual answer
27:43 of people who oppose so that would be a
27:46 good way of describing the bias in that question
